What is 1/3 [2ln(x+3)+ln(x)+ln(x^2-1)] ?

The solution to 1/3 [2ln(x+3)+ln(x)+ln(x^2-1)] is 1/3 ln(x(x+3)^2(x^2-1))

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simplify 1/3 [2ln(x+3)+ln(x)+ln(x^2-1)]

simplify

\frac{1}{3} [2 ln (x + 3) + ln (x) + ln (x^{2} - 1)]

\frac{1}{3} ln (x (x + 3)^{2} (x^{2} - 1))

Solution steps

\frac{1}{3} [2 ln (x + 3) + ln (x) + ln (x^{2} - 1)]

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x + 3) = ln ((x + 3)^{2})

= \frac{1}{3} [ln ((x + 3)^{2}) + ln (x) + ln (x^{2} - 1)]

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln ((x + 3)^{2}) + ln (x) = ln (x (x + 3)^{2})

= \frac{1}{3} [ln ((x + 3)^{2} x) + ln (x^{2} - 1)]

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x (x + 3)^{2}) + ln (x^{2} - 1) = ln (x (x + 3)^{2} (x^{2} - 1))

= \frac{1}{3} [ln ((x + 3)^{2} x (x^{2} - 1))]

Remove parentheses:

(a) = a

= \frac{1}{3} ln ((x + 3)^{2} x (x^{2} - 1))

3.8 + lo g_{10} (\frac{0.19}{0.41})

lo g_{10} (\frac{y}{100})

ln (\frac{1}{2 x ^{3}})

lo g_{8} (64 x) + lo g_{8} (x)

ln ((\frac{y - 1}{4})^{2})

What is 1/3 [2ln(x+3)+ln(x)+ln(x^2-1)] ?
The solution to 1/3 [2ln(x+3)+ln(x)+ln(x^2-1)] is 1/3 ln(x(x+3)^2(x^2-1))